Thanks for the thought-provoking post. How would you answer this criticism of the frequentist paradigm:

• Frequentist methods cannot make statements about actual data, only about abstract properties of the data.

For example, suppose I generated a data set of 1000 samples by weighing a bunch of people. So I just have 1000 numbers x1, x2... x1000 representing their weight in kilograms. Given this data set, frequentist analysis can make various claims about abstract properties such as its mean or variance or whether it could possibly have been drawn from a certain null-hypothesis distribution. But say I simply want to know what is the probability that P(x > 200), ie when I go out and weigh a new person the result will be greater than 200 kg. I claim that frequentist methods simply cannot answer this question; and any method that claims to answer it is actually a Bayesian method in disguise, in particular, it is implicitly using a prior.